Related papers: Disordered statistical physics in low dimensions: …
The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure $\psi(\beta)$. The inverse-temperature like variable $\beta$ allows one to scan the structure of the probability distribution in…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments…
Heterogeneous media constitute random disordered environments where transport is drastically hindered. Employing extensive molecular dynamics simulations, we investigate the spatio-temporal dynamics of tracer particles in the Lorentz model…
These are notes for a mini-course on the extremes of correlated random fields which I gave in the spring 2013 in Marseille. The first chapter recalls the paradigmatic random energy models with finitely many scales introduced by B. Derrida…
The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal…
We study numerically the influence of disorder and localization effects on the local spectroscopic characteristics and infrared optical properties of $\mbox{Ga}_{1-x}\mbox{Mn}_x\mbox{As}$. We treat the band structure and disorder effects at…
We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random masses…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
In a one-dimensional (1D) disordered potential, quantum interferences leading to Anderson lo-calization are ubiquitous, such that all wave-functions are exponentially localized. Moreover, no phase transition toward delocalization is…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…
We introduce novel characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…
We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering…
Ultracold atoms in optical lattices offer a unique platform for investigating disorder-driven phenomena. While static disordered site potentials have been explored in a number of optical lattice experiments, a more general control over…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…